Answer
3D Vector Analysis in a Rectangular Prism
Topic: Vector Component Form and Magnitude Calculation
🧊 Given Dimensions
The rectangular prism is placed in the 3D coordinate system with:
- Length along x-axis: 9 m
- Width along y-axis: 14 m
- Height along z-axis: 11 m
🔮 Purple Vector ( &vec;m; )
📌 Coordinates
Start: (0, 0, 11)
End: (9, 14, 0)
📐 Component Form
&vec;m; = ⟨9, 14, -11⟩
📏 Magnitude
|&vec;m;| = √(9² + 14² + (-11)²) = √398 ≈ 19.95 m
🔷 Blue Vector ( &vec;b; )
📌 Coordinates
Start: (9, 0, 0)
End: (0, 14, 0)
📐 Component Form
&vec;b; = ⟨-9, 14, 0⟩
📏 Magnitude
|&vec;b;| = √((-9)² + 14² + 0²) = √277 ≈ 16.64 m
📊 Summary Table
| Vector | Component Form | Magnitude |
|---|---|---|
🔮 &vec;m; |
⟨9, 14, −11⟩ | 19.95 m |
🔷 &vec;b; |
⟨−9, 14, 0⟩ | 16.64 m |